WASHINGTON — President Obama took a victory lap at the close of the enrollment period for ObamaCare, declaring the controversial law “here to stay” as he announced that his administration had exceeded its goal with 7.1 million sign-ups.

“The debate over repealing this law is over. The Affordable Care Act is here to stay,” Obama told a crowd of lawmakers and supporters at a White House event with the vibe of a pep rally.

The administration met the milestone — which the White House had downplayed earlier this year when the disastrous rollout blocked applications — after a surge of visits to the Web site in the final days before the midnight Monday deadline.

Even with snafus Monday, the site drew nearly 5 million visits, while 2 million people dialed call centers, the White House said.

But the administration has yet to release key data that will reveal whether the effort succeeds long-term, or whether premiums are likely to jump.

Health and Human Services Secretary Kathleen Sebelius said Monday that insurers were reporting that between 80 and 90 percent of people who signed up had paid.

In one positive statistic, the New York exchange reported that 70 percent of 865,000 enrollees were previously uninsured.

Even as he championed the accomplishment, Obama laced his remarks with self-deprecating jibes and admissions of stumbles during the rough rollout of the new law.

The president said there was no “sugar-coating” the botched rollout.

“The Affordable Care Act has not totally fixed our long-broken health-care system,” Obama said. “But it has made the system a lot better.”

People who missed the deadline must wait until November to enroll, unless they have a life-changing event like the loss of a job. But those who got stuck in traffic on the site can still be covered for the next two weeks under a special enrollment process that relies on the honor system.